Carbon dioxide from the atmosphere will easily dissolve in water. Because carbon dioxide passes readily between water and the atmosphere the two reservoirs remain globally in a steady state.
The amount of dissolved carbon the water can hold depends on its temperature. Cold water can dissolve more carbon dioxide than warm water. And the rate at which carbon dioxide is removed from the air depends partly on the activities of water plants and phytoplankton.
These organisms remove carbon dioxide from the water, and more gas dissolves from the air to replace it.
Solid forms of carbon can also dissolve. When creatures from the surface of the ocean die, their bodies sink, along with calcium carbonate skeletons and other particles. As the debris rains down, some of the calcium carbonate dissolves back into the deep ocean water.